1. Field of the Invention
The invention relates to dual-mode thickness-shear quartz pressure sensors. More particularly, the invention relates to dual-mode thickness-shear quartz pressure sensors having a disc as the sensing resonator and external flats for increased pressure sensitivity.
2. State of the Art
Quartz crystals exhibit a physical phenomenon called the piezoelectric effect. When a quartz crystal is subjected to alternate compressive and tensile strains, opposite electric charges are produced on different faces of the crystal. Conversely, when alternating electric charges are applied to opposite faces of the crystal, the crystal expands and contracts alternatingly. This property of quartz has been exploited to produce highly accurate oscillators for audio, video, and telecommunications electronics. Quartz crystals have also been used to produce very accurate clocks.
Quartz crystal resonators consist of a quartz plate mounted between two electrodes. Originally the quartz plates were made from natural quartz, but today cultured quartz is used almost exclusively. The plates (also called wafers or blanks) are fabricated at a precise orientation with respect to the crystallographic axes of the quartz material. This is most often achieved by growing a monolithic block of quartz and then cutting it. The orientation or "cut" of the plate determines frequency-temperature characteristics and other important properties of the resonator.
The quartz plate has many modes of vibration, such as flexure, longitudinal or thickness-extension, face-shear, and thickness-shear, each of which has numerous resonances. Properly oriented electrodes excite the desired mode of vibration. Except for the low-frequency tuning fork resonators used in quartz watches and clocks, most resonators use a thickness-shear mode of vibration. Thickness-shear resonators are classified as high-frequency resonators, while other types are classified as low-frequency resonators. The fundamental frequency of a thickness-shear resonator is inversely proportional to its thickness. There are additional resonances at the 3rd, 5th, etc. overtones, whose frequencies are approximate, but not exact, odd multiples of the fundamental resonance frequency. Resonators are ordinarily designed to optimize the characteristics of one or another of these resonances, such as the fundamental or the third overtone, but the other overtones necessarily still exist.
The resonant frequency of a thickness-shear quartz resonator changes when the ambient temperature or pressure changes. The effects of pressure and temperature on these resonators have been exhaustively studied with the objective of eliminating these effects on oscillators in frequency control applications. Knowledge of these effects has also been used to create piezoelectric transducers.
Piezoelectric pressure and temperature transducers (sensors) have been known for many years. These transducers generally include a crystal blank inside a housing with electrodes placed on opposite sides of the blank. An alternating voltage is applied to the blank which causes it to vibrate at a resonant frequency. The resonant frequency at which the crystal vibrates changes when the crystal is subjected to stresses. Accordingly, changes in temperature and pressure on the housing produce detectible changes in the resonant frequency of the crystal. An exemplary piezoelectric transducer is disclosed in U.S. Pat. No. 3,617,780 to Benjaminson. A similar resonator is shown schematically in prior art FIG. 1. The transducer 10 includes a unitary piezoelectric crystal resonator 12 and cylindrical housing structure 14. The resonator 12 is located on a median radial plane of the housing 14 and crystal end caps 16, 18 are used to cover the open ends of the cylindrical housing 14. Electrodes 20, 22 are located on opposite faces of the resonator 12. The electrodes are typically formed by vacuum deposition of conductive material such as copper or preferably gold. FIG. 1 shows the end caps detached. Typically, the transducer 10 is assembled by gluing the end caps 16, 18 to the cylindrical housing 14 in a rarefied atmosphere leaving a vacuum inside the assembled structure. The transducer is sensitive to changes in temperature and pressure. However, in order to effectively measure either temperature or pressure, one must be held constant or must be known. Pressure sensors of this type are typically used in conjunction with a separate temperature sensor so that the pressure sensor signal can be adjusted to compensate for the effects of temperature on the pressure transducer. Piezoelectric transducers of this type are often referred to as "single mode transducers".
In a material such as piezoelectric quartz, measurable vibration of the resonator plate actually takes place according to three modes, namely, mode A (the quasi-longitudinal mode) and modes B and C (two quasi-transverse or thickness-shear modes). These three modes are distinguished by their frequencies, mode A being the fastest and mode C being the slowest. It is possible to favor some of these modes at the expense of others by suitable choice of the cut and dimensions of the resonator plate. The so-called "single mode" transducers are designed to favor one of the two thickness-shear modes.
One popular solution to the disadvantages of the so-called "single mode transducers" is to provide a quartz resonator in which oscillation in both the B and C modes is favored. This is made possible by carefully selecting the precise orientation of the resonator blank with respect to the crystallographic axes of the quartz material. This orientation, known as the "cut", is described with reference to X, Y, and Z axes where X is the electrical axis, Y is the mechanical axis, and Z is the optical axis of the crystal. Prior art FIG. 2 illustrates these X, Y, and Z axes and a crystal cut defined by the axes X", Y", Z". According to this cut, the axes of the resonator are determined by a first angular displacement .PHI. about the X axis and a second angular displacement .theta. about the Z axis. As shown in FIG. 2, the first angular displacement results in the axes X', Y', Z' with the Z' axis being collinear with the Z axis. The second angular displacement results in the axes X", Y", Z" with the X" axis being collinear with the X' axis. This .PHI., .theta. angular displacement is typical of several popular cuts, including the "SC" (stress compensated) cut (.PHI.=22.5.degree., .theta.=34.3.degree.) and the "WAD" (without activity dip) cut (.PHI.=24.degree., .theta.=33.degree.).
Temperature induced frequency shifts in quartz resonators are significantly different for various harmonic and anharmonic overtones. The amplitude of vibration of a desired mode may be drastically reduced at some temperatures if a neighboring unwanted mode frequency gets close to the frequency of the desired mode. This phenomenon is known as "activity dip". The WAD cut is close to the SC cut but has no activity dips in the B-mode at higher temperatures.
Popular "singly rotated" cuts are also defined by .PHI. and .theta. but with .PHI.=0.degree.. These include the "AT" (A-mode temperature compensated) cut (.PHI.=0.degree., .theta.=35.25.degree.) and the "BT" (B-mode temperature compensated) cut (.PHI.=0.degree., .theta.=-49.22.degree.). The singly rotated cuts result in single mode resonators whereas the doubly rotated cuts result in dual-mode resonators.
The advantage of a dual-mode transducer over a single mode transducer is that B-mode vibration is primarily only responsive to temperature whereas C-mode vibration is responsive to both temperature and pressure. Thus, by noting the change in frequency in both modes, one can solve for both temperature and pressure. Co-owned U.S. Pat. No. 4,419,600 to Sinha discloses dual-mode transducers which are capable of measuring pressure and temperature simultaneously.
Many advances in the science of quartz pressure/temperature transducers have been made in connection with hydrocarbon reservoir modeling. Transient or dynamic pressure measurements are routinely employed in the estimation of formation permeability, reservoir pressure, formation continuity, and reservoir boundaries. The pressures encountered during such modeling can be greater than 20,000 psi. While making measurements, the transducers can be subjected to temperatures of approximately 175.degree. C. The state of the art transducers used in hydrocarbon reservoir modeling are only able to measure pressures up to about 18,000 psi.